Basis of Direct Product of two vector spaces

[rustic plank]

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omeganebula

omeganebula

[rustic plank]

I have proved that this set is linearly independent but how do I prove that it is maximal

ping me if anyone replies

[amber aurora]

Write any (u, v) in U x V as a linear combination of your basis candidate

If U x V is endowed with component-wise addition and component-wise scalar multiplication, it should not be too tough

By doing that, you show that your family of vectors is a spanning set

[rustic plank]

Oh

[rustic plank]

ok ig that works ty

+close

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